9.4 Relative Velocity
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Figure 9.22: Example 9.12 ([3], pp. 355) and substitute θ˙ = ω0 so that rω0 cos θ rω0 cos θ q ωAB = β˙ = = 2 l cos β l 1 − r sin2 θ l2
Differentiate again to get the acceleration relationship:
lβ¨ cos β − lβ˙ 2 sin β = r θ¨ cos θ − r θ˙2 sin θ ˙ θ, ˙ and θ¨ = 0 so that and substitute β, β, αAB
9.4
rω 2 lβ˙ 2 sin β − r θ˙2 sin θ = 0 sin θ = β¨ = l cos β l 1−
r2 l2 r2 l2
−1
sin2 θ
3/2
Relative Velocity
Another method to analyze the kinematics problems is the principle of relative motion. It is usually suitable for the complex motion as it is more scalable and more systematic. Consider first the velocity of points in a rigid body. Velocity propagation in the rigid body Referring to chapter 7, the relative velocity equation using the non-rotating reference frame is vA = vB + vA/B (9.11) Let the two points A and B be on the same rigid body. The implication of this choice is that the motion of one point as seen by an observer translating with the other point must be circular since the radial distance to the observed point from the reference point does not change. Chulalongkorn University
Phongsaen PITAKWATCHARA